Question: Simplify the following expression: $k = \dfrac{-2r^2 - 14r - 20}{r + 5} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-2$ , so we can rewrite the expression: $ k =\dfrac{-2(r^2 + 7r + 10)}{r + 5} $ Then we factor the remaining polynomial: $r^2 + {7}r + {10} $ ${5} + {2} = {7}$ ${5} \times {2} = {10}$ $ (r + {5}) (r + {2}) $ This gives us a factored expression: $\dfrac{-2(r + {5}) (r + {2})}{r + 5}$ We can divide the numerator and denominator by $(r - 5)$ on condition that $r \neq -5$ Therefore $k = -2(r + 2); r \neq -5$